The article considers the right of legislative initiative of the Constitutional Court of the Russian Federation enshrined in the Constitution of the Russian Federation in the light of amendments made to the Fundamental Law of our state in 2020, as well as subsequent updating of special federal constitutional legislation. It is noted that the problem of practice deficiency in implementing the mentioned power by the Constitutional Court of the Russian Federation is not new for the Russian legal science; in general, it is naturally determined and is due to a number of objective factors. However, the process of updating and developing the constitutional provisions on the supreme judicial control body of Russia and, in particular, creating the system of preliminary judicial constitutional control, bring the problem under consideration to a qualitatively new level. The approach itself in terms of granting the mentioned power to supreme courts in the Russian Federation is characterized as atypical for the countries near and far abroad. At the same time, the current lack of practice in exercising the power in question by the Constitutional Court is due to the special role of the latter in the system of supreme state authorities, in particular, the judiciary. The point of view is expressed that the problem cannot be unambiguously solved at the present stage of the statehood development. The author does not share the increasingly expressed point of view today that the right of legislative initiative should be excluded from the powers of the Constitutional Court of the Russian Federation, since this will lead to a violation of the equality of the constitutional and legal statuses of the two independent supreme judicial authorities. In addition, the shortcomings in the wording of certain constitutional provisions have been identified and possible ways to eliminate them have been proposed.